Samples of data and population

Question

 I understand that all samples of data are going to vary from time to time and some of them maybe the same, if the population is higher in one distribution than the other. Do you think that sample of means would still normal or do you think that the sample of means would have to be adjusted to fit within the parameters?

Answer 1

Yes, the sample means from a normal distribution would still be normal, as long as they are random & independent samples. We know this because of the Central Limit Theorem. I'm sure you can find that theorem in your statistics book, if you want more details of why that's true. We also know that the sampling distribution of the mean is normal, in fact: the higher N goes, the more normal the sampling distribution of the means becomes! Isn't that cool!

In general, one may start with any distribution and the sampling distribution of the sample mean will increasingly resemble the bell-shaped normal curve as the sample size increases. This is the content of the Central Limit Theorem.